Section 56. Whenever under the authority of any law two or more municipalities have joint property in, or the right of joint control of, any marine fisheries referred to in section fifty-two, the board of aldermen or city council of the city, or the selectmen of the town if so authorized by the town, in which such fisheries lie may exclusively exercise all the rights, privileges and authority conferred by said section with respect to such fisheries, make appropriations therefor as provided in section fifty-four and exercise such other control, privileges and responsibilities as are granted in other sections of this chapter pertinent thereto, as though such joint control or property did not exist; provided that in the exercise of such rights, privileges, responsibilities and authority such board of aldermen, city council or selectmen shall grant to the citizens of such other municipalities the same rights and privileges as are granted to the citizens of their city or town.